System and method for estimating and optimizing transaction costs

ABSTRACT

A method and system for forecasting the transaction cost of a portfolio trade execution that may be applied to any given trade strategy or an optimal trade strategy that minimizes transaction costs. In preferred embodiments, a server comprises one or more computers that act as an automated forecaster whereby it accepts user-defined input variables from customers and generates a transaction cost estimation report based on those variables. The server is programmed with specific transaction cost estimation and optimization algorithms that model the transaction costs of a specific trade execution based on the user&#39;s trading profile and market variables.

FIELD OF THE INVENTION

This invention relates generally to securities markets, and moreparticularly relates to a system and method for estimating thetransaction costs of a trade execution and developing an optimizedtrading strategy for securities in advance of trading.

BACKGROUND OF THE INVENTION

Securities portfolio transactions typically incur transaction costsarising not only from commissions and bid-offer spreads, but also fromprice movements (market impact) associated with execution. Executioncosts can be large, especially when compared against gross returns, andmight substantially reduce or even eliminate the notional returns to aparticular investment strategy.¹ A large body of research (Keim andMadhavan (1998) provide a survey) shows that market or price impact is amajor component of total trading cost. Consequently, minimization oftransaction costs has been a long-standing aim, especially for tradershandling portfolio transactions; e.g., transactions that rebalancesecurities positions in a portfolio over a specified period of time. Arelated goal is to develop optimal trading strategies to minimizetrading costs or some other objective criterion. ¹For an equallyweighted global portfolio of stocks, turned over twice a year, suchcosts alone account for 23 percent of returns over recent history. SeeDomowitz, Glen, and Madhavan, “Liquidity, Volatility, and Equity TradingCosts Across Countries and Over Time,” working paper, Pennsylvania StateUniversity, January, (2001) for discussion, analysis, and precisedefinitions of cost.

To this end, statistical and mathematical models have been developed inan attempt to forecast the transaction costs of a proposed portfoliotrade execution. These models typically build on some known empiricalfacts about trading costs. For example, empirical studies haveestablished that costs increase in trade difficulty, a factorsystematically related to order size (relative to average tradingvolumes), venue (e.g., Exchange Listed Trades vs. Over The Counter(“OTC”)), trade direction (Buys vs. Sells), firm size (MarketCapitalization), Risk (e.g., the volatility of security returns), andprice level. In addition, costs are also systematically related totrading style, as reported by Keim and Madhavan (1998). Traders whotrade passively (using limit orders and spreading their trades over along period of time) incur lower costs, on average, than traders whotrade more aggressively using market orders to demand immediacy. Twootherwise identical orders might have very different trading costsdepending on how a trader presents them to the market. See Madhavan(2000) for details.

Of the many statistical and mathematical forecasting models developed,most suffer from the inability to perform comprehensive analyses oftransaction costs because the level of trade difficulty and the impactof trading style (e.g., horizon over which trading takes place) is notanalyzed or not accurately analyzed. Therefore, there is a need in thefield to include in a forecasting model an adjustment factor thataccurately accounts for trade difficulty and market conditions, allowingfor a valid comparison of trades executed in different circumstances andtrading conditions. It is important that this system accommodateparameters for trading style. Since the trader's style is closelyrelated to their ultimate objectives (e.g., a value trader might tradepassively over several days to minimize price impact costs, toleratingthe risk of adverse price movements in the interim), this creates a needfor a model that ties strategy to a trader's subjective assessment ofrisk. In particular, there is a need in the field to provide a modelthat would recommend an optimal trading strategy to a trader based onthe trader's risk tolerance and other considerations such as the horizonover which the trade is to be completed. In order to meet these needsand to overcome deficiencies in the field, the present invention enablesportfolio traders to forecast the transaction costs of a proposed tradeexecution based on a user-selected trading style and inputs pertainingto order characteristics and trade difficulty. The invention alsoprovides an optimized trading strategy to satisfy user-definedconstraints.

SUMMARY OF THE INVENTION

The present invention provides a system for forecasting the price impactcosts of a trade execution that may be applied to any given tradestrategy.

The present invention provides an Agency Cost Estimator (“ACE”) methodand system comprising two parts: a first part that comprisescomputer-based models that allow a user to obtain price impact costestimates for any pre-specified strategy, and a second part thatcomprises computer-executed mathematical models that generate an optimaltrading strategy subject to certain assumptions about the user'sultimate objectives.

In another aspect of the present invention, a server comprises one ormore computers that act as an automated forecaster whereby a computeraccepts a user-specified trade strategy and input variables from acustomer and generates a transaction cost analysis or estimation basedon those variables and market data. The server is programmed withspecific transaction cost analysis and optimization algorithms thatmodel the transaction costs of a proposed trade execution based on theuser's risk aversion profile, characteristics of the proposed tradeexecution, and market variables. The servers may be connected to aplurality of customers over a communication network, such as theInternet, and customers enter their strategy profile and hypotheticaltrade order characteristics through the communication network to theserver associated with transaction cost optimization. In yet anotheraspect of the present invention, the transaction cost analysis web siteallows a user to perform inquires and calculations in real-time.According to another aspect of the present invention, the transactioncost analysis process is adapted to provide a direct interface to asecurities price database to enable the display of transaction costanalysis results in “real-time.”

In another aspect of the present invention, the transaction costanalysis allows for intra-day calculation of price-based benchmarks.

According to another aspect, the invention provides a method forestimating and/or optimizing transaction costs for a proposed tradeorder for a security. The method comprises the steps of providing aserver connected to a communication network, the server being programmedwith a specific transaction cost optimization and/or estimationalgorithm; receiving at the server over the network a proposed tradeorder from a customer; calculating the estimated transaction costs forthe proposed order according to the specific trading strategy of thecustomer and the transaction cost estimation algorithm; and providing anestimation report to the customer over the network.

In preferred embodiments of the present invention, multiple servers maybe deployed where each server accepts proposed orders and other customerinput data directly over the communication network from customerswishing to estimate the transaction costs of one or more securities tobe traded according to the particular trading strategy set by thecustomer. All servers have access to multiple trading destinations,access to real-time and historical market data, and real-time analyticdata. Furthermore, each server has access to other servers on thecommunication network such that market and historical data, orcompilations of data, can be exchanged between the servers, and theservers can inter-operate more efficiently. The user can edit or modifythe proposed trading strategy received from the cost estimator, thensend the resulting trade list to a trading venue or to an automatedtrading system such as ITG Inc's VWAP Smart Server.

The present invention will become more fully understood from theforthcoming detailed description of preferred embodiments read inconjunction with the accompanying drawings. Both the detaileddescription and the drawings are given by way of illustration only, andare not limitative of the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a system for forecasting transaction costsfor a proposed trade execution according to a specific trading strategyand according to a preferred embodiment of the invention; and

FIG. 2 is a flow diagram of an exemplary system for estimating andoptimizing the transaction costs of a trade execution carried out undera specific trading strategy according to the invention.

DETAILED DESCRIPTION OF THE INVENTION

The present invention embodies a transaction cost estimation method andsystem comprising a first part having computer-based price impact andvolatility models that allow a user to obtain transaction cost estimatesfor any given strategy, and a second part comprising computer-executedmathematical models that generate an optimal strategy based on certainassumptions and the results of the first part.

Referring to FIG. 1, one or more transaction cost optimization servers11 is provided on a communication network 10. The network 10 may be apublic network or a private dedicated network. A server 11 is programmedwith transaction cost estimation and optimization algorithms, and hasaccess to various trading mechanisms or exchanges through the network10, such as the New York Stock Exchange (NYSE) 18, the POSIT® intra-dayequity matching system 20, the over-the-counter (OTC) market 22(including, but not limited to, the NASDAQ stock market), or anelectronic communications network (ECN) 24.

According to preferred embodiments of the present invention, the server11 is electronically accessible directly by customers through thenetwork 10. This access can be either through a personal computer (PC)12 or a dedicated client terminal 16 which is electronically connectedto the network 10 such as via the Internet or a dedicated line.Alternatively, clients could interact with the network via a tradingdesk 14 through which a customer can perform a transaction costanalysis. Particularly, the trading desk is a user interface thatprovides comprehensive agency trading services utilizing multipleliquidity sources.

According to preferred embodiments of the present invention, a number ofdifferent servers 11 may be provided on the network, with each server 11running a transaction cost analysis program and having access to variousappropriate trading forums and various electronic communicationnetworks. A customer may submit a proposed portfolio trade execution foranalysis with any specific one of the servers 11. A server 11 receivesthe proposed portfolio trade execution from the customer over thenetwork 10 and processes and analyzes the execution according to theuser-selected preset trading strategy algorithm being run by the server11. The server 11 then executes the transaction cost analysis andoptimization and preferably transmits the execution results to thecustomer in real time.

By providing such servers, a significant advantage over the prior artsystem (where analyses are executed manually by human traders or bycomputer using outdated information) is achieved. The server 11 canhandle much more complex trades including trades involving large volumesand many more different equities. Additionally, the server 11 canprovide expert results for a very large number of equities, unlike atrader who may be able to concentrate on or follow only a relativelysmall number of equities at once. A server according to the presentinvention has a further advantage over a human trader in that it can beelectronically connected via the network 10 to a real time marketinformation provider 15 as well as sources providing historical andderived market data such that it can receive and process multipleindicators on a continuous basis. Further, multiple requests fortransaction cost analysis having different desired trading strategies(e.g., levels of risk aversion) can be simultaneously executed byrouting proposed portfolio trade orders to the appropriate server 11.

FIG. 2 illustrates one example of a system for estimating and optimizingthe transaction costs of a trade execution according to the invention,wherein transaction costs are estimated according to a transaction costestimation and optimization algorithms. The ACE algorithms areprogrammed into a server 11, and customers wishing to execute the ACEtransaction cost estimation and optimization for proposed portfoliotrades input requests for analyses and transmit them directly to the ACEserver. The ACE server performs one or more transaction cost analyses(TCA).

According to this method, at step 201 the customer's orderspecifications are retrieved. For example, a customer may wish to sell 1million shares of security XYZ. At step 202, the customer specifies (andinputs) a value for the risk aversion parameter (RAP). If no value isretrieved, the program sets the default value to 0.4. At step 203, thecustomer specifies the optimal trade time horizon, e.g., selling 1million shares of XYZ security over 7 days. At step 204, the programretrieves market parameters, e.g., security master information (i.e.,ticker symbol, cusip, exchange) closing price, volatility, and tradingvolume. At step 205, the program calculates estimations for thecustomer's set of parameters and system inputs based on the most recentmarket data. At step 206, the results are displayed to the customer as atable of expected costs and standard deviation of costs for differentRAP values. At step 207, the customer selects a pair of values (EC andSD) from the table that are most appropriate in the particular case, anda value of RAP corresponding to the chosen pair of values. At step 208,the customer inputs the new RAP value (while maintaining the otherparameters) to see a new set of expected cost and cost standarddeviation. This establishes a range of cost estimates. At step 209, theprogram calculates (and displays) the optimal trade strategies based onthe customer's inputted parameters, from which the customer may choosethe strategy that best fits the customer's particular situation.

As can be seen from FIG. 2, The agency cost estimator (ACE) method andsystem is a computer-executed set of statistical models that forecaststhe transaction costs of a trade execution. In ACE, cost is measured asthe difference between the average execution price and the prevailingprice at the start of order execution. ACE can be used to:

-   Provide estimates of the price impact cost for any specified trading    strategy-   Form pre-trade cost benchmarks to evaluate the execution performance    of traders and brokers, calibrated to a variety of common    pre-specified strategies (constant fraction of average daily volume,    VWAP-strategy) or any arbitrary user-defined strategy-   Evaluate the costs of trading as a function of the desired trading    strategy of a trader-   Fine tune a trading strategy in terms of trading horizon and    aggressiveness-   Recommend an optimal trading strategy that balances execution costs    against the uncertainty in the realized cost of trading-   Generate a confidence interval which contains the realized cost    Unlike many other conventional products, ACE is a dynamic model that    recognizes that a trader will typically break an order into several    trades to minimize execution costs.    Three significant features of ACE are as follows:

ACE recognizes that agency traders incur price impact because a trademoves the prevailing price when he/she executes a trade. It is the costof demanding liquidity. Price impact has both permanent and temporarycomponents. The permanent component is information based; it capturesthe persistent price change as a result of the information conveyed tothe market that the trade occurred. The temporary price impact istransitory in nature; it is the additional liquidity concession to getthe liquidity provider to take the order into inventory. The permanentimpact means that the first trade of a multi-trade order will affect theprices of all subsequent sub-blocks sent to the market. Modeling thisdynamic link is a key element of computing the price impact for aprogram of trades spread over time.

ACE also recognizes that there is no such thing as “the” cost estimatefor a trade. In reality, cost is a function of the trader's strategy.The more aggressive the trading strategy, the higher the cost.Aggressiveness can be measured in terms of how rapidly the trader wantsto execute the trade given the trade's size relative to normalliquidity. Thus, the ACE estimate is predicated on a particular tradingstrategy. ACE 2.0 recognizes several benchmark strategies and alsoallows the user to specify any arbitrary trading strategy. These includeVWAP (a participation strategy that mimics the volume pattern in thesecurity based on historical data), uniform (a flat or linear strategy),the optimal ACE strategy (described below), or any user-specified customstrategy. ACE can also be used to develop an “optimal strategy” thatbalances price impact costs against opportunity costs. Opportunity costsare largely due to price volatility and create uncertainty in therealized cost of trading as they do for the realized return ofinvesting. When executing an agency order the balance between priceimpact and opportunity cost is chosen on the basis of the motivation forthe order, which ultimately comes from the investment manager. Passivemanagers are mainly concerned about price impact. Growth or momentummanagers are more worried about opportunity costs. We refer to theinvestment manager's sensitivity to opportunity costs as his/her riskaversion, just as is done for an investment manager's sensitivity toinvestment risk. The ACE model estimates the expected cost and thestandard deviation of the cost of the agency trading strategy thatoptimally balances the tradeoff between paying price impact andincurring opportunity costs for a given level of risk aversion andtrading horizon. The user can either define the weight on risk directlyor by telling ACE the fraction of the order to be completed bymid-horizon. It does so by expressing the trading problem as amulti-period stochastic control problem. It then calculates the expectedcost and the standard deviation of the cost for the resulting optimalstrategy. This strategy is recommended for traders who want to weightthe opportunity cost associated with trading over a long interval oftime.

The ACE model is not a purely econometric model. Rather, it is astructural model that uses parameters estimated from econometric modelsof agency trade execution. In particular, ACE relies on stock specificeconometric models of volatility and price impact. ACE uses marketparameters as an input, including security master information (ticker,cusip, exchange), closing price, volatility, trading volume, bid/askspread, distribution of trading volume and volatility by 30 minuteintraday bin (based on latest available market data for several months).We estimate volatility as the standard deviation of returns for the mostrecent 60 trading days, volume as the 21-day median dollar volume, andbid/ask spread as the 5-day average time and size weighted bid/askspread. These approaches allows us to take into account the latesttrends in stock price behavior and at the same time to filter outfluctuations, which often are generated by market news, earningsannouncements and other factors.

ACE model is a tool to reliably forecast transaction cost andstatistical characteristics of this forecast for a scenario selected bya user. The ACE estimate depends on the user's strategy and tradingaggressiveness. Further, the model is a dynamic one that assumes tradingthrough market orders. It is not intended to be a model of upstairstrading costs or block pricing. The agency cost estimator and optimizerof the present invention is unique in that it allows the user to specifya particular trading style as the basis for estimation of costs.

An important aspect of the ACE model and system is that it can be usedto recommend a particular trading strategy for a user. ACE balances twoconsiderations: expected cost and standard deviation. The ACE modelestimates the expected cost (“EC”) and the standard deviation (“SD”) ofthe cost of the agency trading strategy that optimally balances thetradeoff between paying price impact (in consideration for liquiditydemand) and incurring opportunity costs for a user-specified weights oncost and risk and trading horizon. It does so by expressing the tradingproblem as a multi-period stochastic control problem. It then calculatesthe expected cost and the standard deviation of the cost for theresulting optimal strategy.

The execution cost is a signed (i.e., positive or negative) differencebetween the value of a security or portfolio of securities at thebeginning and the end of the specified trading horizon. The ACE modelestimates the expected cost of the agency trading strategy as follows:

The trading horizon is first divided into a number of bins, or timeperiods of equal duration. For example, in the U.S. market, ACEconsiders thirteen bins of 30 minute duration per trading day. However,any number of bins of any duration may be used so long as the binparameters are appropriately configured for the chosen duration. Thetrading horizon may consist of several trading days, with an arbitrarystarting bin in the first day and ending bin in the last day. The tradeorder is defined by its trading horizon, trade side (buy or sell), sizeand trading strategy (sequence of share quantities per bin for a giventrading horizon). Trading of all share quantities specified for each binis assumed to be completed within the respective bin.

The ACE model distinguishes between market price, defined as a securitymid-quote price or average of bid and ask quote prices, and an averageexecution price for which a given bin share quantity was executed. Theaverage execution price includes temporary price impact and averageprice improvement. A temporary price impact represents a liquidityconcession made to induce the taking of an order into inventory,typically half the prevailing bid-ask spread (net of any priceimprovement). A permanent price impact is the effect on market price (ascontrasted with trade price) caused by the execution of the trade. Largesize trades affect market price not only within the execution period,but have a persistent effect to the end of the trading day.

Price improvement is a price received that is better than the prevailingprices (i.e., bid for a sell order or ask for a buy order). Generally,all buyer/seller initiated orders are expected to execute at theprevailing ask/bid quote price. However, a buyer/seller often mayreceive a better execution price than the prevailing ask/bid quote priceat the time the order was placed, due to sudden and unpredictable marketmoves. Such better received price is defined as a price improvement.

For any given security, volume and price volatility vary significantlyby bin within the same trading day. The volume and volatilitydistributions by bin are determined statistically and taken into accountwhen estimating transaction cost and generating an optimal strategy.While volume and volatility distributions for a particular stock ideallyshould be used when estimating transactions costs for that stock,research has demonstrated that such distributions may be unstable, evenfor very liquid stocks, because of market noise. Consequently, as analternative aggregated bin distributions of a larger number of stocksmay be used. Such aggregated distributions have been shown to be muchmore stable.

The total realized transaction cost C can be defined as

$\begin{matrix}{C = {\sum\limits_{i = 1}^{T}\; \left\lbrack {{C_{i}\left( n_{i} \right)} + {\left( {\alpha + {\varepsilon_{i}\sigma} + {T_{i}n_{i}}} \right)x_{i}}} \right\rbrack}} & (1)\end{matrix}$

where

n_(i)=total number of shares traded on day i

α=expected daily price change

ε_(i)=random price disturbance for day i

σ=standard deviation of daily price change

T_(i)=linear coefficient for price impact persistence after trade on dayi

x_(i)=residual at the end of day i

The mean or expected cost EC may be considered as simply an averagevalue of total cost if the execution could be repeated many times, sincethe total execution cost C is a stochastic or random variable ratherthan a deterministic value or number. This is so because total executioncost is subject to a large number of unknown factors, includinguncertain behavior of other market participants, market movementsrelated to macroeconomic or stock-specific factors, etc. EC may bedefined as

$\begin{matrix}{{{EC} = {\sum\limits_{i = 1}^{T}\; \left\lbrack {{{EC}_{i}\left( n_{i} \right)} + \left( {{\alpha \; x_{i}} + {T_{i}n_{i}x_{i}}} \right)} \right\rbrack}},} & (2) \\{where} & \; \\{{{{EC}_{i}\left( n_{i} \right)} = {{\sum\limits_{j = 1}^{N}\; \left\lbrack {{C_{i}\left( n_{i,j} \right)}^{2} + {\left( {\alpha_{j} + {\gamma_{j}n_{i,j}}} \right){\overset{\sim}{x}}_{i,j}}} \right\rbrack} + {\left( {\alpha_{0} + J} \right)n_{i}}}},} & (3)\end{matrix}$

α_(j)=standard deviation of price change in bin j

α_(o)=standard deviation of price change between closing and opening

γ_(j)=linear coefficient for price impact persistence after trade in binj

n_(i,j)=shares traded in bin j of day i

J=half bid-ask spread

{tilde over (x)}_(i,j)=residual for the day after bin j of day i

N=number of bins in trading horizon

In the first use of ACE, computing a cost of a pre-specified tradingstrategy, equations (2) and (3) are used to generate a predicted cost.Specifically, given a pre-specified distribution of shares across thetrading horizon, by bin, given by {n}, we compute the expected price ineach bin using (3) and then sum across bins (weighting by ni) using (2)to get total cost. A proprietary daily risk model is used to get aforward looking estimate of the variance of cost, allowing for thepossibility of price movements across bins.

In the second use of ACE, the optimal trading strategy, denoted by {n*},is computed by solving a particular optimization problem that balancesexpected cost against variance. The optimization problem of ACE is thengiven as:

PD=min{(1−λ)EC+λ*VarC},

where λ is a non-negative parameter called the risk aversion parameter(or weight on opportunity cost), and Var C is the variance or square ofthe standard deviation of cost C. The weight on opportunity cost istypically input by the user and is a number between 0 and 1; very lowweights correspond to styles of trading where opportunity costs are nota significant consideration (e.g., a value trader without information),whereas high values correspond to aggressive trading styles (e.g., atrader who is concerned about adverse price movements) where trading isaccomplished rapidly.

The ACE optimal strategy is a solution of the optimization problem. Notethat ACE requires the user to select a value of risk aversion parameterthat reflects the user's risk tolerance level, in addition to tradinghorizon for the specific transaction to be executed. The risk aversionparameter does not have an absolute value, i.e., a value whichrepresents a user's risk aversion level for one particular scenario doesnot necessarily represent the same level for another one. Rather, RAPidentifies a scenario within the same order. Because RAP doesn't have anabsolute value, two parameters must be taken into account for eachscenario under consideration: the expected cost (EC) and the standarddeviation (SD) of a trading strategy. For an aggressive strategy,expected cost is relatively higher, but standard deviation is lower.Therefore, on average, expected cost is slightly higher than for lessaggressive strategies, but the level of uncertainty is lower, that is,the range of possible values of cost around expected cost is somewhatnarrow.

The ACE model and system does not suggest aggressive or passivestrategies. Rather, ACE provides optimal strategies and correspondingparameter forecasts for all different scenarios and allows a user toselect a scenario which best fits the trader's particular situation. Forexample, if it is more important for a trader not to exceed a certainreasonable level of transaction cost rather than minimize the averagecost (e.g., if a trader is penalized for under-performance and notcredited for over-performance), it is suggested to use more aggressivestrategies. For each value of risk aversion, ACE will calculate expectedcost and standard deviation of expected cost, and will generate anoptimal trade execution strategy for the selected trading horizon.

In contrast to the prior art, the ACE model is not a purely econometricmodel, but rather a structural model that uses parameters estimated fromeconometric models of agency trade execution. In particular, the ACEmodel relies on stock-specific econometric models of volatility andprice impact. ACE uses market parameters as an input, including securitymaster information (ticker, cusip, exchange), closing price, volatility,trading volume, bid/ask spread, distribution of trading volume andvolatility by 30 minute intraday bin.

The ACE model also accounts for market volatility. The ACE modelestimates volatility as the standard deviation of price returns for themost recent 60 trading days, volume as the 21-day median dollar volume,and bid/ask spread as the 5-day average time and size weighted bid/askspread. These approaches take into account the latest trends in stockprice behavior, and at the same time filter out fluctuations, whichoften are generated by market news, earnings announcements and otherfactors.

The ACE model and system considers specific effects from calendarmilestones, such as the end of a month, quarter or year, or the effectof a holiday or Monday, when volatility is usually higher as a result ofnews disseminated from a company announcement or from over the weekend.

A unique aspect of the present invention is the model's consideration ofsingle stocks as a single name case. Particularly, the single name caseconsiders a trade for a single stock, in isolation from any other ordersthe user may be executing at the same time. The inputs for the singlename case may include, inter alia, ticker symbol (or cusip), side (buyor sell), number of shares to trade, trading horizon, risk aversionparameter, and starting bin.

The ACE model also considers the trading horizon in analyzing a proposedportfolio trade execution. If there is no requirement on selection oftrading horizon for an order, it may be selected as an optimal one. Anoptimal trading horizon is defined as:

min{k=1,2, . . . :p66_(k) /p66_(k+1)<1.05},

where p66_(k)—66%-percentile of cost for k-day trading horizon.

For example, if a trader trades 1 million shares of security XYZ and theACE system sets the optimal horizon to be equal to 6, it means that fora 7 day trading horizon the 66%-percentile of transaction cost dropsless than 5% of its value, compared against the 6-day horizon. For fewerthan 6 days, it drops more than 5%, if comparing 66%-percentile oftransaction cost for any two consecutive days. This definition, however,does not restrict users who would prefer another optimal tradinghorizon. They may run the ACE program for several consecutive numbers ofdays and apply their own definition.

Example 1 Executing a Single Name Case.

In this example, the system and method considers a trade for a singlestock, in isolation from any other orders the user may be executing atthe same time. The user (trader) may access the computer program througha user interface (UI), and the program executes according to thefollowing steps:

1. The user selects all parameters according to the trader's orderspecifications and any reasonable value of RAP. By default, 0.4 is usedas the value for RAP. In most cases, this particular value suggests amoderately aggressive strategy, which is typically appropriate for aninitial run. The user then selects the “Calculate” command, e.g., byclicking on a “calculate” button on the user interface. The softwareprogram will display ACE estimates for the user's set of parameters andsystem inputs based on the most recent (e.g., real time) market data.

2. The user accesses the Risk Frontier screen. A table is presented withvalues of EC and SD for different values of RAP. The user selects a pairof values (EC, SD) from the table that are the most appropriate in theparticular case, and a value of RAP corresponding to the chosen pair ofvalues. The user may change the values for Lower and Upper Limits andStep. The user may select the Draw Chart option (e.g., a button or icon)to select an appropriate chart to graphically represent the range ofvalues.

3. After selecting the most appropriate pair (EC, SD) and correspondingRAP value, the user may return to the Cost Estimates screen. The userinputs the selected RAP value and then selects the “Calculate” button.

4. The user may go to the Trade Strategy screen to view the optimaltrade strategy. The user may select the chart button to view adistribution by interval within a selected day or by trading day, if thetrading horizon consists of more than one trading day. The user may goto the Shares Frontier screen to change the size of the order to studyhow it will affect the ACE cost estimation estimates. The user maychange the values for Lower and Upper Limits and a Step, and then selectthe Draw Chart button to choose an appropriate range of share values.

Example 2 Executing a List Case.

In this example, the system and method considers a trade for a list ofstocks in a portfolio. The list case is designed for portfolio trading.In the list case, the ACE method and system includes a risk model, whichtakes into account correlation between price movements for all stocks ina portfolio. The list case has the same inputs as the single name case,except it uses a portfolio list instead of a security symbol. As withthe single name case, the user (trader) may access the computer programthrough a user interface, and the program executes according to thesteps outlined in Example 1.

The user may obtain estimates for a default set of parameters and mayconsider different values of RAP from the Risk Aversion Frontier screenin the same fashion as was performed in the single name case. The usermay select the appropriate set of values for a particular case value.Trade horizon also can be adjusted as desired.

The ACE model and system generates a pre-trade report as part of apreliminary analysis of a proposed portfolio trade. The pretrade reportis designed to run a list of trades as a set of separate “stand-alone”trades. The pre-trade report includes a list of single name cases.Entering a list of trades is performed in the same manner as the listcase in Example 2. As with the other cases, in the pre-trade reportcase, a user may select an appropriate value of RAP, which should be thesame for all trades in the list.

Portfolio Characteristics Report

The ACE model also can generate a portfolio characteristics report thatdescribes the risk characteristics of the portfolio. The model uses aproprietary daily risk model to construct forecasts of the returnvolatility of the portfolio (the standard deviation of the return of theportfolio on a daily basis, relative to a user-selected benchmarkportfolio such as the S&P 400, etc.) and risk characteristics. Inparticular, the report shows the percentage of the portfolio's value bysector (e.g., raw materials, etc.) as well as select statistics. Seeattached screen shot.

Optimization of Transaction Cost

In addition to portfolio transaction cost estimation, the ACE method andsystem comprises an algorithm that calculates an optimal trade strategythat minimizes transaction costs. As described above, the inventiongenerally comprises two parts: A first part based on price impact andvolatility models that allows a user to obtain transaction costestimates for any given strategy, and a second part comprising analgorithm that builds an optimal strategy based on the results of thefirst part.

After randomly simulating millions of strategies and for each strategycalculating the value of the criteria based on the expected cost and thestandard deviation of the cost for a strategy, an optimal strategy withthe lowest value of the criteria was selected. That is, by performing asignificant number of simulations, a very close approximation of theoptimal strategy provided by ACE was discovered. Such a simulation wasperformed, and it demonstrated that ACE method and system provides anoptimal trading strategy. In fact, after millions of repetitions, nostrategy was obtained that provided a lower value of the criteria thanthe ACE strategy provided.

An optimal strategy is a subject of model definitions and assumptions.The ACE optimal strategy is “optimal” only for a user's specificcriteria, e.g., level of risk aversion, and under the assumption thatexpected cost and standard deviation are estimated correctly. Thecorrectness of the assumptions was tested and verified using historicalorder execution data.

The validity of the ACE model was proven by testing how well the modelestimated the expected cost and the standard deviation of the cost for aset of orders traded consistently using a fixed strategy. The testvalidated the estimated daily volatility as well as the estimatedcoefficients for the price impact functions. For the order executionhistory, data was collected from ITG Inc.'s VWAP (Volume WeightedAverage Price) SmartServer because the orders are completed in asystematic way by always trading a given fraction of the target in everyhalf-hour bin of the day. The data comprised a set of all ordersexecuted through the VWAP server during a period of 10 months. For eachorder, the number of shares traded during each half-hour bin and theaverage execution price was obtained. Certain orders were excluded,e.g., orders that constituted less than 1% of the 21-day median volume,orders that had short sales, or for which there was a separate,simultaneous order in the same security. The sample size comprised11,852 orders. The data set covered 1,304 exchange-listed securities and49 NASDAQ securities.

The transaction cost per share was defined as the difference between theaverage execution price and the price available at the beginning of thetrading period (the benchmark price). The sign (positive or negative) ofthe difference was used so that a positive value represented a badoutcome. For each order t in the data set, the realized transaction costx_(t) is computed. Also calculated, using the parameters of the ACEmodel, is the estimated expected transaction cost m_(t) and theestimated standard deviation of the cost s_(t). The variablez_(t)=(x_(t)−m_(t))/s_(t) is referred to as the normalized excess cost.The random variable z_(t) is expected to have the mean of 0 and thestandard deviation of 1. A t-test is performed for the hypothesis thatthe mean of z_(t) is 0 assuming that standard deviation is unknown, anda chi-square test for the hypothesis that the standard deviation ofz_(t) is 1 assuming that the mean is unknown.

In general, statistical tests are used under the same assumptions thatsamples they are run on have been built. ACE assumes that the expecteddaily return, called á for all stocks, is 0. Standard deviation ishigher for months when the market was very volatile (see Table 1).However, for a relatively stable market, positive and negative effectswill compensate each other, and it is appropriate to use the sample totest at least the mean of the normalized excess cost. From thisperspective, the test is considered a benchmark of the model'sapplicability. Tests were performed for the entire order data set andseveral subsets of the data. The data was divided into subsets, e.g., bymonth, trade share volume relative to 21-day median volume, 21-daymedian volume, 5-day average spread, 5-day average spread relative toprice, volatility (60-day standard deviation) of daily percentage pricereturns and share price.

The results are provided in the tables below. The “Mean” and “StandDev”in the tables represent the mean and standard deviation of thenormalized excess cost, respectively.

TABLE 1 T-Test Results by Month month December January February MarchJuly August 1998 1999 1999 1999 1999 1999 Number of orders 1,150 8841,611 1,834 975 1,020 Mean 0.001 −0.016 0.007 −0.003 −0.006 −0.029p-value 0.979 0.602 0.811 0.906 0.862 0.330 StandDev 0.773 0.888 1.1201.020 0.992 0.943 month September November December 1999 October 19991999 1999 all number of orders 942 900 1,146 1,390 11,852 Mean 0.0100.011 −0.018 −0.003 −0.004 p-value 0.831 0.818 0.596 0.906 0.680StandDev 1.393 1.432 1.168 1.127 1,093Overall, the mean of normalized excess cost is very close to the desiredvalue of zero. Thus, on average the ACE model accurately forecastedtrading costs for the sample. Moreover, the relatively high p-valuesmean that one cannot distinguish, in a statistical sense, the smallvalues from zero.

TABLE 2 T-test Results by Percentage of 21-day Median Daily Share Volume% 1-4% 5-9% 10-14% 15-19% 20%+ all 5%+ Number 8,857 2,434 422 112 2711,852 2,995 of orders Mean −0.006 −0.002 0.011 0.031 −0.069 −0.0040.0007 p-value 0.62 0.94 0.84 0.76 0.79 0.68 0.97 StandDev 1.088 1.1171.078 1.093 1.281 1.093 1.111Even though the mean actual cost increases with trade size (as amultiple of the 21-day median trading volume), the mean normalizedexcess cost stays close to 0. This indicates that the model isforecasting the correct magnitude of the cost across orders of widelyvarying liquidity. The p-value for orders of 1-4% of the 21-day mediandaily share volume is the lowest among all subgroups. It stays inlinewith the fact that the influence of other factors for price movementcompared to the influence of the order execution is relatively weakerfor small trades than for relatively large trades. For example,considering only samples for orders of the magnitude higher than 4% ofthe 21-day median trading volume (see last column of the Table 4), theestimated mean equals 0.0007 and the p-value is 0.97. Tables 3-7 presentthe results of T-tests for other subsets of data.

TABLE 3 T-test Results by 21-Day Median of Daily Share Volume volume (inthousands) <50 50-100 100-250 25-500 500-1,000 >1,000 all number of1,095 1,319 3,237 2,913 1,798 1,490 11,852 orders Mean −0.422 0.0180.006 0.005 0.010 0.005 −0.004 p-value 0.19 0.60 0.76 0.80 0.71 0.870.68 StandDev 1.055 1.260 1.048 1.083 1.098 1.074 1.093

TABLE 4 Table 4: T-test Results by Absolute Value of Spread spread (incents) Lower Between Between Between Between higher than 10 10 and 13 14and 16 17 and 20 21 and 30 than 30 all Number of 1,448 3,617 3,610 2,264840 73 11,852 orders Mean 0.007 0.000 −0.006 0.000 −0.345 −0.135 −0.004p-value 0.80 1.00 0.76 0.98 0.33 0.30 0.680 StandDev 1.102 1.084 1.1621.010 1.030 1.093 1.093

TABLE 5 T-test Results by Spread Relative to Price Spread to price %<0.2% 0.2%-0.3% 0.3%-0.4% 0.4%-0.5% 0.5%-0.7% 0.7%-1% >1% all Number of636 2,269 2,597 2,036 2,465 1,174 675 11,852 orders Mean 0.052 0.005−0.018 −0.000 −0.009 −0.009 −0.022 −0.004 p-value 0.21 0.80 0.40 1.000.68 0.83 0.60 0.680 StandDev 1.043 1.013 1,089 1.041 1.089 1,342 1.1101.093

TABLE 6 T-test Results by Volatility Relative to Price Volatility toprice percentage <1% 1-2% 2-3% 3-4% 4-5% >5% all Number of 270 5,4364,527 1,314 240 65 11,852 orders Mean −0.016 −0.005 0.004 −0.021 −0.010−0.086 −0.004 p-value 0.82 0.75 0.80 0.46 0.86 0.34 0.680 StandDev 1.1771.166 1.037 1.005 0.877 0.709 1.093 Volatility to price percentage <5050-100 100-250 25-500 500-1,000 >1,000 all Number of orders 1,095 1,3193,237 2,913 1,798 1,490 11,852 Mean −0.422 0.018 0.006 0.005 0.010 0.005−0.004 p-value 0.19 0.60 0.76 0.80 0.71 0.87 0.68 StandDev 1.055 1.2601.048 1.083 1.098 1.074 1.093

TABLE 7 T-test Results by Price Price (in dollars) 5-15 15-30 30-5050-100 >100 all Number of orders 1,124 4,134 3,938 2,467 189 11,852 Mean−0.010 −0.004 −0.009 −0.002 0.093 −0.004 p-value 0.78 0.84 0.59 0.930.17 0.680 StandDev 1.170 1.142 1.064 1.032 0.923 1.093

The results strongly validate the parameters behind the ACE model. Thep-value is relatively low only for the most illiquid stocks, in terms ofextreme values of price, median volume or volatility. However, it isnever low enough to reject the null hypothesis that the normalizedexcess cost is different from 0.

As can be readily seen by an person of ordinary skill in the art, inalternative embodiments of the present invention proposed tradeexecutions can be automatically transferred within the network from oneserver operating according to a first trade strategy algorithm toanother server having a second different trade strategy algorithm.

The invention being thus described, it will be apparent to those skilledin the art that the same may be varied in many ways without departingfrom the spirit and scope of the invention. Any and all suchmodifications are intended to be included within the scope of thefollowing claims.

1. A method for estimating transaction costs of a security tradeexecution according to a trading strategy selected by a user, comprisingthe steps of: providing a server connected to a communication network,said server being programmed with a specific strategy transaction costoptimization algorithm; receiving at said server over said network datadefining parameters of a proposed trade execution from a user, and dataspecifying a user-selected trading strategy; and estimating thetransaction costs of the received proposed trade execution based on theuser-selected trading strategy and market data, and recommending actionsdetermined by said specific strategy transaction cost optimizationalgorithm that minimize said transaction costs under said user-selectedtrading strategy, whereby a user may minimize transaction costs bytaking said actions in executing said trade; wherein, said user-selectedtrading strategy may be selected from among a plurality of predefinedtrading styles, or may be specifically defined by said user.
 2. Themethod of claim 1, wherein the method further comprises providing anestimation report to the customer over the network.
 3. The method ofclaim 1, wherein an adjustment factor adjusts for trade difficulty andmarket conditions to allow for an accurate comparison of tradesperformed under different circumstances and trading conditions.
 4. Themethod of claim 1, wherein said adjustment factor provides an expectedtrading cost for each security for each day based on a statisticalanalysis of measures of trade difficulty.
 5. The method of claim 1,wherein a plurality of servers are connected to a plurality of customersover a communication network, and customers enter their risk aversionprofile and hypothetical trade order characteristics through thecommunication network to the server associated with transaction costoptimization.
 6. The method of claim 1, comprising the further step of:providing a user interface to allow a user to identify relevant data andtrends in a dataset, and to locate factors that affect transactionperformance.
 7. The method of claim 6, wherein a user is able to changea subset of the dataset under consideration and perform real-timeanalytic calculations without additional pre-processing.
 8. The methodof claim 6, wherein a user may add new user aggregates, withoutadditional pre-processing.
 9. The method of claim 1, wherein the serveris adapted to provide a direct interface to a securities price databaseto enable the display of transaction cost analysis results in real-time.10. The method of claim 1, wherein the transaction cost algorithm allowsfor intra-day calculation of price-based benchmarks.
 11. The method ofclaim 5, wherein each server accepts proposed orders and other customerinput data directly over the communication network from customerswishing to estimate the transaction costs of one or more securities tobe traded according to the particular trading strategy set by thecustomer, and all servers have access to multiple trading destinations,access to real-time and historical market data, and real-time analyticdata, and each server has access to other servers on the communicationnetwork such that market and historical data, or compilations of data,can be exchanged between the servers, and the servers can interoperatemore efficiently.
 12. A method according to claim 1, wherein saidtransaction cost estimation takes into account temporary price impact,permanent price impact, and price improvement factors.
 13. A methodaccording to claim 1, wherein said transaction cost estimationrecommends specific share quantity trade executions for each of a numberof time duration bins according to the trading strategy selected by theuser, to optimize transaction costs under said selected tradingstrategy.
 14. A system for estimating and optimizing transaction costsof proposed execution trades of securities according to a risk valueselected by a user, comprising: a plurality of servers, each serverbeing programmed with a specific transaction cost estimation andoptimization algorithm, receiving from said user data specifyingparameters of a proposed trade order and estimating the transactioncosts of the received proposed trade execution based on theuser-selected risk value and market data, and recommending actionsdetermined by said specific strategy transaction cost optimizationalgorithm that minimize said transaction costs under said user-selectedrisk value, whereby a user may minimize transaction costs by taking saidactions in executing said trade; said plurality of servers beingconnected to a plurality of clients over a communication network,wherein a user enters at a client a selected risk value and dataspecifying parameters of a proposed trade order and transmits them fromsaid client over said communication network to a server associated withthe transaction cost estimation and optimization, and receives saidestimation of transaction costs according to a selected from said serverover said communication network.